The latest version, 4.1., can be jailbroken. You won't be able to upgrade without starting fresh though; just restore from a backup afterward to bring back your texts, SMS messages, etc.
If you don't rely on an unlock for an unofficial carrier, simply update to 4.1 and then jailbreak with either greenpois0n or limera1n.
If you do rely on an unlock, you'll need to use custom firmware from PwnageTool (if you are on Windows, use the latest redsn0w and then point it to the custom 4.1 firmware).
It will be like a brand new iphone. You can always sync back contacts, pictures, videos, songs and so forth. Only jailkbreak apps will be gone and you will have to reinstall again.